Answer:
1. Each teacher has 13 children.
2. 64 colors
3. 33
4. 60
Step-by-step explanation:
Solution:
1. Step 1: Divisibility Rules
52 is divisible by:
2 - ✔ 7 - ✖ 3 - ✖ 8 - ✖
4 - ✔ 9 - ✖ 5 - ✖ 10 - ✖
6 - ✖
Therefore, 52 is divisible by 2 and 4.
Step 2: Multiples
List down the multiples of 2 and 4.
2, 4, 6, 8, 10
4, 8, 12, 16, 20
The LCM of 2 and 4 is 4.
Thus, there are 4 teachers at the center.
Step 3: Divide
number of children ÷ number of teachers =?
52 ÷ 4 = 13
2. 9240 = 2 * 2 * 2 * 3 * 5 * 7 * 11
=> 9240 = 2³ * 3¹ * 5¹ * 7¹ * 11¹
Total possible Factors
= ( 3 + 1)(1 + 1)( 1+ 1)(1 + 1)(1 + 1)
= 4(2)(2)(2)(2)
3. et x - be the number
y - be the quotient
then,
= y +
9[ = y + ]
x = 9y + 6 (1)
= y +
4[ = y + ]
x = 4y + 1 (2)
=y +
10[ = y + ]
x = 10y + 3 (3)
Solve for y using equations 1 and 3.
9y + 6 = 10y + 3
9y - 10y = -6 + 3
-y = -3
-1[y = -3]
y = 3
Using y = 3, find x in equation 1.
x = 9y + 6
x = 9(3) + 6
x = 27 + 6
x = 33
Therefore, the number we are looking for is 33.
To check:
33 ÷ 9 = 3 remainder 6
33 ÷ 4 = 8 remainder 1
33 ÷ 10 = 3 remainder 3
